Finite Group Databasebeta

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C13×C25×#157 #26043323

order11700
isoclinismisoclinic class of #157
automorphism?
homologyAbelianization (H1) = C4×C13×C25 · Schur multiplier (H2) = C3

Aliases

direct productC13×C25×#157

Splittings

Fitting, HallC32×C13×C25 ⋊ C4
derived, SylowC32 ⋊ C4×C13×C25
HallC32×C25 ⋊ C4×C13
HallC32×C13 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC13×C25#157
commutator, hypocenterC32C4×C13×C25
FrattiniC5C5×C13×#157
FittingC32×C13×C25C4
socleC32×C5×C13C4×C5
prime radicalC5×C13×C3⋊D3C2×C5
cosocleC5×C3⋊D3C2×C5×C13
LCSG ▷ C32
UCSC1 ◁ C13×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11700, 170);